Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x+8y &= -5 \\ -4x-4y &= 5\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-4y = 4x+5$ Divide both sides by $-4$ to isolate $y$ $y = {-x - \dfrac{5}{4}}$ Substitute this expression for $y$ in the first equation. $-2x+8({-x - \dfrac{5}{4}}) = -5$ $-2x - 8x - 10 = -5$ Simplify by combining terms, then solve for $x$ $-10x - 10 = -5$ $-10x = 5$ $x = -\dfrac{1}{2}$ Substitute $-\dfrac{1}{2}$ for $x$ back into the top equation. $-2( -\dfrac{1}{2})+8y = -5$ $1+8y = -5$ $8y = -6$ $y = -\dfrac{3}{4}$ The solution is $\enspace x = -\dfrac{1}{2}, \enspace y = -\dfrac{3}{4}$.